Question

find a. the mean; b. the deviation from the mean for each data item; and c. the sum of the deviations in part (b) for the following group of data items. 158, 160, 167, 169, 171 a. the mean is 165. (simplify your answer.) b. complete the following table by entering the deviations for each data value. (simplify your answers.)

Explanation:

Part a: Mean Calculation

Step 1: Sum the data items

The data items are 158, 160, 167, 169, 171. We sum them up: \(158 + 160 + 167 + 169 + 171\)
First, \(158+160 = 318\), then \(318+167 = 485\), then \(485+169 = 654\), then \(654+171 = 825\)

Step 2: Divide by the number of items

There are 5 data items. So the mean is \(\frac{825}{5}\)
\(\frac{825}{5}=165\)

Step 1: Deviation for 158

Deviation = \(158 - 165\)
\(158 - 165=-7\)

Step 2: Deviation for 160

Deviation = \(160 - 165\)
\(160 - 165=-5\)

Step 3: Deviation for 167

Deviation = \(167 - 165\)
\(167 - 165 = 2\)

Step 4: Deviation for 169

Deviation = \(169 - 165\)
\(169 - 165 = 4\)

Step 5: Deviation for 171

Deviation = \(171 - 165\)
\(171 - 165 = 6\)

Step 1: Sum the deviations

The deviations are -7, -5, 2, 4, 6. We sum them up: \(-7 + (-5)+2 + 4 + 6\)
First, \(-7+(-5)=-12\), then \(-12 + 2=-10\), then \(-10 + 4=-6\), then \(-6 + 6 = 0\)

Answer:

The mean is \(\boldsymbol{165}\)

Part b: Deviation Calculation (Deviation = Data Item - Mean)